Kinematics and Dynamics Model via Explicit Direct and Trigonometric Elimination of Kinematic Constraints
The efficient implementation of kinematics and dynamics models is a key to model based control of mechatronic systems such as robots and wearable assistive devices. This paper presents an approach for the derivation of these models in symbolic form for constrained systems based on the explicit elimination of the kinematic constraints using substitution variables with trigonometric expressions and the Lagrange equations of the second kind. This represents an alternative solution to using the implicit form of the constraints or using the explicit elimination at comparable computational effort. The method is applied to a novel exoskeleton designed for craftsmen force assistance, which consists of multiple planar closed kinematic loops and gear mechanisms.
Keywordsdynamics closed-loop Lagrangian equations substitution variables explicit form trigonometric expressions
Unable to display preview. Download preview PDF.
The presented work was funded by the Federal Ministry of Education and Research of Germany (BMBF) under grant number 16SV6175 and has also received funding from European Union’s Horizon 2020 research and innovation programme under grant agreement No. 688857 (“SoftPro”).
- 1.Wehage, R., Haug, E.: Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems. Journal of mechanical design 104(1), 247–255 (1982). DOI https://doi.org/10.1115/1.3256318
- 2.Nakamura, Y., Ghodoussi, M.: Dynamics computation of closed-link robot mechanisms with nonredundant and redundant actuators. IEEE Transactions on Robotics and Automation (1989). DOI https://doi.org/10.1109/70.34765
- 3.Luh, J., Zheng, Y.F.: Computation of input generalized forces for robots with closed kinematic chain mechanisms. IEEE Journal on Robotics and Automation 1(2), 95–103 (1985). DOI https://doi.org/10.1109/JRA.1985.1087008
- 4.Udwadia, F.E., Kalaba, R.E.: A new perspective on constrained motion. Proceedings: Mathematical and Physical Sciences pp. 407–410 (1992). DOI https://doi.org/10.1098/rspa.1992.0158
- 5.Samin, J.C., Fisette, P.: Symbolic modeling of multibody systems, vol. 112. Springer Science & Business Media (2013). DOI https://doi.org/10.1007/978-94-017-0287-4
- 6.Khalil, W., Vijayalingam, A., et al.: OpenSYMORO: An open-source software package for Symbolic Modelling of Robots. In: IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 1206–1211. Besançon, France (2014). DOI https://doi.org/10.1109/AIM.2014.6878246
- 7.Park, F., Choi, J., Ploen, S.: Symbolic formulation of closed chain dynamics in independent coordinates. Mechanism and machine theory 34(5), 731–751 (1999). DOI https://doi.org/10.1016/S0094-114X(98)00052-4
- 8.Khalil, W., Bennis, F.: Symbolic calculation of the base inertial parameters of closed-loop robots. The International journal of robotics research 14(2), 112–128 (1995). DOI https://doi.org/10.1177/027836499501400202
- 9.Nülle, K., Schappler, M., et al.: Projektabschlussbericht ”3. Arm”. Tech. rep., Mechatronik Zentrum Hannover (2017). DOI https://doi.org/10.2314/GBV:1014030161
- 10.Atkinson, L.: A simple benchmark of various math operations (2014). Online: http://www.latkin.org/blog/2014/11/09/, accessed 20.08.2018
- 11.Hindriksen, V.: How expensive is an operation on a CPU? (2012). Online: https://streamhpc.com/blog/2012-07-16/, accessed 20.08.2018